We define the intensity I of a wave , or the power per unit area, to be the rate at which the energy being transported by the wave transfers through a unit area A perpendicular to the direction of travel of the wave
The intensity of sound decreases as we move farther from the source. We identify an imaginary sphere of radius r centered on the source. When a source emits sound equally in all directions, we describe the result as a spherical wave. The average power, P av emitted by the source must be distributed uniformly over this spherical surface of area 4∏ r 2 . Hence, the wave intensity at a distance r from the source is
If the source in motion, the wave fronts heard by the observer are closer together than they would be if the source were not moving. As a result, the wavelength λ ’ measured by observer A is shorter than the wavelength
λ of the source, the source moves at distance :v s .T = v s /f and the wavelength is shortened by this amount.
(a)Shock wave produced when a source moves from So to Sn with a speed v s , which is greater than the wave speed v in the medium. The envelope of the wave fronts forms a cone whose apex half-angle is given by sin θ = v / v s . (b) A stroboscopic photograph of a bullet moving at supersonic speed through the hot air above a candle.
The V -shaped bow wave of a boat is formed because the boat speed is greater than the speed of the water waves it generates.
Analogous to a shock wave formed by an airplane traveling faster than sound. Jet airplanes traveling at supersonic speeds produce shock waves. The shock wave carries a great deal of energy concentrated on the surface of the cone. Such shock waves are unpleasant to hear and can cause damage to buildings when aircraft fly supersonically at low altitudes.